Question

Find the derivative using the limit definition calculator a) Evaluating the function at a specific point

b) Finding the slope of a tangent line at a point
c) Estimating the area under the curve
d) Computing the average rate of change over an interval

Answer 1

The derivative of a function can be used to evaluate the function at a specific point, find the slope of a tangent line at a point, estimate the area under the curve, and compute the average rate of change over an interval.

Step-by-step explanation:

The derivative of a function can be used in various ways:

1. Evaluating the function at a specific point: By finding the derivative of a function at a specific point, we can determine the rate of change of the function at that point.
2. Finding the slope of a tangent line at a point: The derivative gives us the slope of the tangent line to the graph of a function at a specific point, which represents the instantaneous rate of change of the function at that point.
3. Estimating the area under the curve: The derivative can be used to estimate the area under a curve by dividing it into smaller intervals and approximating the shape of each interval.
4. Computing the average rate of change over an interval: The derivative allows us to calculate the average rate of change of a function over an interval by finding the slope of the secant line that connects the endpoints of the interval.